July 1998

Example  5. The Brazilian Gross National Product series has 33 quarterly
            observations.  This is quite short for time series modeling.
            Consequently, adding or changing regressors often has a
            signficant impact on other coefficent estimates and on the
            seasonal factors.  Estimated coefficients often appear to be
            statistically significant.

	    Try replacing the one-coefficient weekday-weekend day trading
            day model td1nolpyear with tdnolpyear and look at the impact.
            Try other regressors, for example, Easter effect regressors.
            Do you think that Easter effects or day of week effects can
            be estimated reliably from 33 observations?  Do some experiments
            to test this.

	    To add a specified regression effect to a series, you can
            specify the b vector in the regression spec with coefficients
            fixed at -1 times the values you want to impose.  When X-12-ARIMA
            subtracts the fixed regression effect from the original series,
            it will add the effect you want.


# Example  5: brazgnp.spc  

# RegARIMA estimation of calendar effects in a short series.

series{
  name="BRAZGNP" 
  start=1990.1
  period=4
  data=(97.49 96.11 106.17 100.23
        91.53 103.51 107.44 101.64
        95.47 101.72 103.71 101.02
        98.73 107.06 109.16 106.77
       103.40 110.38 115.79 116.85
       114.18 117.46 116.99 116.64
       112.57 120.10 123.26 122.17
       116.84 124.82 126.79 124.81
       118.13)
  title="Brazilian GNP"
  decimals=2
}
regression{
  variables=(
             ao1990.2 
#             tdnolpyear
             td1nolpyear
             )
#  aictest=( 
#            easter
#            tdnolpyear
#            )
}
arima{model=(0 1 1)(0 1 1)}
estimate{ }
check{}
#outlier{types=all}
forecast {maxlead=4 print=none}
x11{mode=add}